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Assess Uncertainties

2.8.21The OB-adjusted NPVs provide a starting point for understanding the impact of risk between different options. However, the future is inherently uncertain therefore no matter how thoroughly costs, benefits, risks and timing are identified and analysed, and even after best efforts have been made to adjust for optimism bias, there will remain uncertainty over the accuracy of the assumptions made. It is essential to test how these uncertainties may affect the choice between options. Whereas OB-adjustment is primarily about ensuring NPVs are based on best estimates, assessment of uncertainty is chiefly about testing the robustness of the appraisal conclusions.
2.8.22Sensitivity analysis is the key technique for this purpose and it is fundamental to appraisal. It is the process of examining how the balance of advantage among options is affected by reasonable variations in key assumptions. Its purpose is to influence the option selection decision; it is not something to be applied merely to a preferred option after it has been selected. The need for sensitivity analysis should always be considered, and, in practice, dispensed with only in exceptional cases. It is always potentially useful but is particularly valuable when the NPVs of options are relatively close to each other.
2.8.23The basic procedure is to alter an assumption, recalculate the OB-adjusted NPV for each option, and consider the impact on both the total net benefits, and on the balance of advantage between the options.
2.8.24It is generally recommended to consider the effect of varying assumptions one at a time as this helps to isolate the assumptions that have the most impact. Some variations may have little impact on NPVs or option ranking, in which case they may not be regarded as a cause for much concern. Other variations may alter the ranking of options or significantly change the NPV. Such variations should be considered carefully and may require specific risk management actions. For example, it may be appropriate to seek to reduce the uncertainty over particular assumptions in order to make them more robust, and improve the chances of a good outcome. (See section on Risk Reduction Strategies in STEP 6 above).
2.8.25

The calculation of 'switching values' is a particular form of sensitivity test. It shows by how much a variable would have to fall (if it is a benefit) or rise (if it is a cost) to switch the balance of advantage from one option to another, or switch the NPV from positive to negative. This may be a crucial input into the decision as to whether a proposal should proceed. For example, it can help answer key questions such as:

  • By how much can we allow benefits to fall short of expectations, if the project is to remain worthwhile? How likely is this?
  • How much can operating costs increase without jeopardising the VFM of the proposal? How likely is this?
2.8.26

In any particular case, judgement in the light of past experience should be used to decide upon the assumptions that are worth subjecting to sensitivity analysis, and the range of variation to be examined for each assumption. A prior analysis of costs into fixed, step, variable, and semi-variable categories can help in understanding the sensitivity of the total costs of proposals. Examples of the assumptions which should be considered for sensitivity analysis include:

  • projections of need or demand e.g. school enrolments, traffic forecasts, projected sickness incidence rates
  • estimates of key costs and benefits e.g. items of capital or recurrent costs, forecasts of revenue income
  • estimates of land or property valuations, particularly in periods of property market volatility
  • changes in real prices e.g. growth of real wages or real oil prices
  • weights and scores attached to non-monetary factors
  • the phasing of costs or benefits
  • the time horizon for the appraisal
2.8.27The reasons for choosing the assumptions investigated and the range of variations examined should be recorded. Slavish analyses of variations of plus or minus some arbitrary percentage in every assumption should be avoided.
2.8.28Presentation of sensitivity analyses is important, particularly when many are undertaken. Summary tables should generally be provided, comparing the key results of all the sensitivity tests undertaken. Inclusion of large numbers of spreadsheets that repeat most of the rows of figures in the main spreadsheets is not very helpful. Sufficient information should be provided to facilitate checking of sensitivity calculations.
2.8.29

Departments should explain the implications of sensitivity analysis for option selection. It is not good practice simply to append sensitivity analyses to appraisal reports without explaining their significance.

Scenarios and Expected Values
2.8.30It can sometimes be helpful to group potential variations into scenarios, for example, to enable consideration of "optimistic" and "worst case" scenarios. "Scenario planning" looks at the consequences of various possible states of the world for anything from an individual investment project to an entire corporate strategy. Scenario planning supplements sensitivity analysis by describing alternative internally consistent possible future economic and political environment, and outcomes. Scenarios are often useful for planning an investment programme and may also be justified for exceptionally large and complicated projects, or for policies that are very sensitive to the external environment.
2.8.31Scenarios should be chosen to draw attention to the major technical economic and political uncertainties upon which the success of the project or option or strategy depends. Generally the best approach is to set up two or three scenarios that differ in important dimensions. The expected NPV can be calculated for each scenario. It may also be helpful to undertake some sensitivity analysis within and between scenarios.
2.8.32Where there are a number of possible NPV scenarios or outcomes whose probability can be reasonably estimated - or where a number of NPVs are considered to be equally probable - then the Expected Value of NPV should be calculated and used as the base case NPV.
2.8.33The Expected Value NPV is the average of the possible outcomes weighted by their probabilities. For example, suppose there are three scenarios with NPVs and probabilities estimated as follows:

Scenario

NPV

Probability

NPV x Probability

1

£5m

0.2

£1.0m

2

£4m

0.3

£1.2m

3

£3m

0.5

£1.5m

Expected Value:

£3.7m

2.8.34

More sophisticated techniques should be used as appropriate in particularly large or complex appraisals and in PFI projects. For example,

  • in PFI cases, it may be appropriate to use Monte Carlo analysis to calculate expected values rather than single point estimates for NPVs. Specialised computer software and expert assistance may be required.
  • Proposals requiring sequential decisions can be analysed using 'decision trees', which are graphical representations of the set of possible strategies. Different strategies result in different NPVs depending on the events (or states of the world) that occur. An extension of the technique can be employed when the probability of any particular risk is assigned.

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